Well, Ein means there is just one. So while you can certainly say "A public building", you cannot say "A public buildings". It works the same in German, so while you have the right idea for the adjective your second sentence is nonsense.

You can, however, say something like "No public buildings" which is Keine öffentlichen Gebäude. Note that the article is also declined (gets -e) to match the plural.

Be aware also that the declension of the adjective changes if there is no article: "Public buildings" is Öffentliche Gebäude.